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Rationality of moduli of vector bundles on curves

A. D. King·A. H. Schofield
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Abstract

The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational isomorphism is compatible with fixing determinants in M(r,d) and M(h,0) and we obtain as a corollary that the moduli space of bundles of rank r and fixed determinant of degree d is rational, when r and d are coprime. A key ingredient in the proof is the use of a naturally defined Brauer class for the function field of M(r,d).

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A. D. King, A. H. Schofield. 1999-07-12. Rationality of moduli of vector bundles on curves. https://arxiv.org/abs/math/9907068

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